Geodesic
Exact distribution for the generalized F tests
Discussiones Mathematicae. Probability and Statistics, Tome 22 (2002) no. 1-2, pp. 37-51

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Generalized F statistics are the quotients of convex combinations of central chi-squares divided by their degrees of freedom. Exact expressions are obtained for the distribution of these statistics when the degrees of freedom either in the numerator or in the denominator are even. An example is given to show how these expressions may be used to check the accuracy of Monte-Carlo methods in tabling these distributions. Moreover, when carrying out adaptative tests, these expressions enable us to estimate the p-values whenever they are available.
Keywords: exact distribution theory, hypothesis testing, generalized F distribution, adaptative test 
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Fonseca, Miguel; Mexia, Joao; Zmyślony, Roman. Exact distribution for the generalized F tests. Discussiones Mathematicae. Probability and Statistics, Tome 22 (2002) no. 1-2, pp. 37-51. http://geodesic.mathdoc.fr/item/DMPS_2002_22_1-2_a3/